My reflections on some important points about innovation, specifically the application of mathematical principles in new contexts around foundational models, and the evolving nature of technology, data science perhaps AI.

The idea that “if it were possible, it would have already been done” is a common barrier to innovation. Many groundbreaking technologies and methodologies were developed because someone dared to look at an old problem in a new way. Differential equations have been around for centuries, but their application in modern computational systems, like neural networks, is still an area ripe for exploration and innovation.

Why are differential equations not truly used in neural networks? (is this a correct statement) At a fundamental level, neural networks and deep learning involve a lot of calculus, particularly in the form of gradient descent and backpropagation algorithms, where derivatives (gradients) of loss functions are computed to update the weights of the network. This process is deeply connected to differential calculus and, by extension, differential equations. The idea of acceleration and velocity is analogous to understanding how quickly weights in a neural network are changing—this can be crucial for improving learning algorithms and making them more efficient.

I would be very curious to read white papers that explore that, anyone? (please share). My journey in the DS application field for e-commerce, and many years of tech startups did not provide the opportunity to leverage my mathematical background. I guess my high school knowledge would be sufficient.. (HAHA)   

After extensive conversation with ChatGPT, it recommended to look into – neural ordinary differential equations (NODEs). In NODEs, the concept of a neural network is reimagined as a continuous-depth model, described by ordinary differential equations. This approach has shown promise in various applications, offering advantages like adaptive computation and a natural handling of continuous-time data. (Reference: https://arxiv.org/pdf/1806.07366.pdf)

How can one bring differential equations to practical use, food for thought?

The key to integrating differential equations more deeply into machine learning and e-commerce (like personalized recommendations) lies in identifying the right problems where these advanced mathematical tools can provide unique advantages. For example, modeling dynamic systems or processes that change over time in an e-commerce context, such as customer behavior or stock levels, could potentially benefit from differential equations to predict future states more accurately.

So who can be my ideal customer for ODEs in neural nets..